Paper # Author Title
We suggest that one way in which economic analysis is useful is by offering a critique of reasoning. According to this view, economic theory may be useful not only by providing predictions, but also by pointing out weaknesses of arguments. It is argued that, when a theory requires a non-trivial act of interpretation, its roles in producing predictions and offering critiques vary in a substantial way. We offer a formal model in which these different roles can be captured. Download Paper
A literal interpretation of neo-classical consumer theory suggests that the consumer solves a very complex problem. In the presence of indivisible goods, the consumer problem is NP-Hard, and it appears unlikely that it can be optimally solved by humans. An alternative approach is suggested, according to which the household chooses how to allocate its budget among product categories without necessarily being compatible with utility maximization. Rather, the household has a set of constraints, and among these it chooses an allocation in a case-based manner, influenced by choices of other, similar households, or of itself in the past. We offer an axiomatization of this model. Download Paper
We propose a formal model of scientific modeling, geared to applications of decision theory and game theory. The model highlights the freedom that modelers have in conceptualizing social phenomena using general paradigms in these fields. It may shed some light on the distinctions between (i) refutation of a theory and a paradigm, (ii) notions of rationality, (iii) modes of application of decision models, and (iv) roles of economics as an academic discipline. Moreover, the model suggests that all four distinctions have some common features that are captured by the model. Download Paper
The art of rhetoric may be defined as changing other people’s minds (opinions, beliefs) without providing them new information. One technique heavily used by rhetoric employs analogies. Using analogies, one may draw the listener’s attention to similarities between cases and to re-organize existing information in a way that highlights certain regularities. In this paper we offer two models of analogies, discuss their theoretical equivalence, and show that finding good analogies is a computationally hard problem. Download Paper
People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are "theoretical cases", which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice and why economists prefer simple cases. Download Paper
People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are “theoretical cases”, which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer complexity arguments that explain why case-based reasoning may sometimes be the method of choice; why economists prefer simple examples; and why a paradigm may be useful even if it does not produce theories. Download Paper
People often wonder why economists analyze models whose assumptions are known to be false, while economists feel that they learn a great deal from such exercises. We suggest that part of the knowledge generated by academic economists is case-based rather than rule-based. That is, instead of offering general rules or theories that should be contrasted with data, economists often analyze models that are “theoretical cases”, which help understand economic problems by drawing analogies between the model and the problem. According to this view, economic models, empirical data, experimental results and other sources of knowledge are all on equal footing, that is, they all provide cases to which a given problem can be compared. We offer some complexity arguments that explain why case-based reasoning may sometimes be the method of choice; why economists prefer simple examples; and why a paradigm may be useful even if it does not produce theories. Download Paper
Economic theory reduces the concept of rationality to internal consistency. As far as beliefs are concerned, rationality is equated with having a prior belief over a “Grand State Space”, describing all possible sources of uncertainties. We argue that this notion is too weak in some senses and too strong in others. It is too weak because it does not distinguish between rational and irrational beliefs. Relatedly, the Bayesian approach, when applied to the Grand State Space, is inherently incapable of describing the formation of prior beliefs. On the other hand, this notion of rationality is too strong because there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of beliefs. Download Paper
Economic modeling assumes, for the most part, that agents are Bayesian, that is, that they entertain probabilistic beliefs, objective or subjective, regarding any event in question.  We argue that the formation of such beliefs calls for a deeper examination and for explicit modeling.  Models of belief formation may enhance our understanding of the probabilistic beliefs when these exist, and may also help up characterize situations in which entertaining such beliefs is neither realistic nor necessarily rational. Download Paper
Economic modeling assumes, for the most part, that agents are Bayesian, that is, that they entertain probabilistic beliefs, objective or subjective, regarding any event in question.  We argue that the formation of such beliefs calls for a deeper examination and for explicit modeling.  Models of belief formation may enhance our understanding of the probabilistic beliefs when these exist, and may also help up characterize situations in which entertaining such beliefs is neither realistic nor necessarily rational. Download Paper
Economic theory reduces the concept of rationality to internal consistency. The practice of economics, however, distinguishes between rational and irrational beliefs. There is therefore an interest in a theory of rational beliefs, and of the process by which beliefs are generated and justified. We argue that the Bayesian approach is unsatisfactory for this purpose, for several reasons. First, the Bayesian approach begins with a prior, and models only a very limited form of learning, namely, Bayesian updating. Thus, it is inherently incapable of describing the formation of prior beliefs. Second, there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. It follows that the Bayesian approach is neither sufficient not necessary for the rationality of  beliefs. Download Paper
People may be surprised by noticing certain regularities that hold in existing knowledge they have had for some time. That is, they may learn without getting new factual information. We argue that this can be partly explained by computational complexity. We show that, given a knowledge base, finding a small set of variables that obtain a certain value of R2 is computationally hard, in the sense that this term is used in computer science. We discuss some of the implications of this result and of fact-free learning in general. Download Paper
Economic theory reduces the concept of rationality to internal consistency. The practice of economics, however, distinguishes between rational and irrational beliefs. There is therefore an interest in a theory of rational beliefs, and of the process by which beliefs are generated and justified. We argue that the Bayesian approach is unsatisfactory for this purpose, for several reasons. First, the Bayesian approach begins with a prior, and models only a very limited form of learning, namely, Bayesian updating. Thus, it is inherently incapable of describing the formation of prior beliefs. Second, there are many situations in which there is not sufficient information for an individual to generate a Bayesian prior. Third, this lack of information is even more acute when we address the beliefs that can be attributed to a society. We hold that one needs to explore other approaches to the representation of information and of beliefs, which may be helpful in describing the formation of Bayesian as well as non-Bayesian beliefs. Download Paper
People may be surprised by noticing certain regularities that hold in existing knowledge they have had for some time. That is, they may learn without getting new factual information. We argue that this can be partly explained by computational complexity. We show that, given a database, finding a small set of variables that obtain a certain value of R2 is computationally hard, in the sense that this term is used in computer science. We discuss some of the implications of this result and of fact-free learning in general. Download Paper
Inductive learning aims at finding general rules that hold true in a database. Targeted learning seeks rules for the prediction of the value of a variable based on the values of others, as in the case of linear or non-parametric regression analysis. Non-targeted learning finds regularities without a specific prediction goal. We model the product of non-targeted learning as rules that state that a certain phenomenon never happens, or that certain conditions necessitate another. For all types of rules, there is a trade-off between the rule's accuracy and its simplicity. Thus rule selection can be viewed as a choice problem, among pairs of degree of accuracy and degree of complexity. However, one cannot in general tell what is the feasible set in the accuracy complexity space. Formally, we show that finding out whether a point belongs to this set is computationally hard. In particular, in the context of linear regression, finding a small set of variables that obtain a certain value of R2 is computationally hard. Computational complexity may explain why a person is not always aware of rules that, if asked, she would find valid. This, in turn, may explain why one can change other people's minds (opinions, beliefs) without providing new information. Download Paper